Clean air_pollution_df:

## 'data.frame':    6468 obs. of  4 variables:
##  $ Country                      : Factor w/ 231 levels "Afghanistan",..: 1 1 1 1 1 1 1 1 1 1 ...
##  $ ISO.alpha3.code              : Factor w/ 197 levels "","AFG","AGO",..: 2 2 2 2 2 2 2 2 2 2 ...
##  $ Year                         : Factor w/ 28 levels "1990","1991",..: 1 2 3 4 5 6 7 8 9 10 ...
##  $ Deaths.Air.Pollution.per.100k: num  299 291 279 279 287 ...

Clean gdp_df:

## tibble [12,401 × 4] (S3: tbl_df/tbl/data.frame)
##  $ Country        : Factor w/ 259 levels "Afghanistan",..: 11 11 11 11 11 11 11 11 11 11 ...
##  $ ISO.alpha3.code: Factor w/ 259 levels "ABW","AFG","AGO",..: 1 1 1 1 1 1 1 1 1 1 ...
##  $ Year           : Factor w/ 60 levels "1960","1961",..: 27 28 29 30 31 32 33 34 35 36 ...
##  $ GDP.USD        : num [1:12401] 405463417 487602458 596423607 695304363 764887117 ...

Clean population_region_df:

## 'data.frame':    16685 obs. of  6 variables:
##  $ SDGRegion           : Factor w/ 9 levels "AUSTRALIA/NEWZEALAND",..: 9 9 9 9 9 9 9 9 9 9 ...
##  $ SubRegion           : Factor w/ 22 levels "AUSTRALIA/NEWZEALAND",..: 5 5 5 5 5 5 5 5 5 5 ...
##  $ Country             : Factor w/ 235 levels "Afghanistan",..: 34 34 34 34 34 34 34 34 34 34 ...
##  $ M49.code            : Factor w/ 235 levels "100","104","108",..: 3 3 3 3 3 3 3 3 3 3 ...
##  $ Year                : Factor w/ 71 levels "1950","1951",..: 1 2 3 4 5 6 7 8 9 10 ...
##  $ Population.thousands: num  2309 2360 2406 2449 2492 ...

Clean population_region_df:

## 'data.frame':    249 obs. of  4 variables:
##  $ Country.or.Area: Factor w/ 249 levels "Afghanistan",..: 6 234 1 10 8 3 12 7 9 11 ...
##  $ ISO.alpha2.code: Factor w/ 248 levels "AD","AE","AF",..: 1 2 3 4 5 6 7 8 9 10 ...
##  $ ISO.alpha3.code: Factor w/ 249 levels "ABW","AFG","AGO",..: 7 8 2 14 4 6 10 3 12 9 ...
##  $ M49.code       : Factor w/ 249 levels "4","8","10","12",..: 6 225 1 8 190 2 16 7 3 10 ...

Clean world:

## tibble [177 × 2] (S3: sf/tbl_df/tbl/data.frame)
##  $ iso_a2: Factor w/ 175 levels "AE","AF","AL",..: 53 162 48 26 165 89 167 124 72 7 ...
##  $ geom  :sfc_MULTIPOLYGON of length 177; first list element: List of 3
##   ..$ :List of 1
##   .. ..$ : num [1:5, 1:2] -180 -180 -180 -180 -180 ...
##   ..$ :List of 1
##   .. ..$ : num [1:9, 1:2] 178 178 177 177 178 ...
##   ..$ :List of 1
##   .. ..$ : num [1:8, 1:2] 180 180 179 179 179 ...
##   ..- attr(*, "class")= chr [1:3] "XY" "MULTIPOLYGON" "sfg"
##  - attr(*, "sf_column")= chr "geom"
##  - attr(*, "agr")= Factor w/ 3 levels "constant","aggregate",..: NA
##   ..- attr(*, "names")= chr "iso_a2"

Note that we only have geometries for 175 countries, some will not be able to be plot on a map but that is okay.

Final DataFrame Construction

Now let’s merge our 4 datasets into one using a series of inner joins using country code and year as keys depending on the specific join. We are using inner joins because we want to drop all null values which would mean either a country does not have a country code or we have more years of data than our smallest year range (the air pollution dataset).

## 'data.frame':    5197 obs. of  12 variables:
##  $ ISO.alpha2.code              : Factor w/ 248 levels "AD","AE","AF",..: 1 1 1 1 1 1 1 1 1 1 ...
##  $ M49.code                     : Factor w/ 249 levels "4","8","10","12",..: 6 6 6 6 6 6 6 6 6 6 ...
##  $ Year                         : Factor w/ 28 levels "1990","1991",..: 23 24 1 2 3 4 5 6 7 8 ...
##  $ ISO.alpha3.code              : Factor w/ 197 levels "","AFG","AGO",..: 5 5 5 5 5 5 5 5 5 5 ...
##  $ Country.x                    : Factor w/ 231 levels "Afghanistan",..: 6 6 6 6 6 6 6 6 6 6 ...
##  $ Deaths.Air.Pollution.per.100k: num  17.7 17.2 29 28.7 28.5 ...
##  $ GDP.USD                      : num  3188808943 3193704343 1029048482 1106928583 1210013652 ...
##  $ SDGRegion                    : Factor w/ 9 levels "AUSTRALIA/NEWZEALAND",..: 4 4 4 4 4 4 4 4 4 4 ...
##  $ SubRegion                    : Factor w/ 22 levels "AUSTRALIA/NEWZEALAND",..: 19 19 19 19 19 19 19 19 19 19 ...
##  $ Population.thousands         : num  82 81 55 57 59 61 63 64 64 64 ...
##  $ geom                         :sfc_MULTIPOLYGON of length 5197; first list element:  list()
##   ..- attr(*, "class")= chr [1:3] "XY" "MULTIPOLYGON" "sfg"
##  $ gdp.per.capita               : num  38887914 39428449 18709972 19419800 20508706 ...

Our dataset is finally ready to be analyzed.

Histogram of Air Pollution Induced Deaths, Population, and GDP per Capita

Figure 5,6,7: Histogram of Air Pollution Induced Deaths, Population, and GDP per Capita.

Looks like deaths.air.pollution.per.100k, population, and gdp.per.capita are not normal and are all right skewed.

Boxplot of Air Pollution Induced Deaths, Population, and GDP per Capita

Let’s look at a boxplot for the outliers.

Figure 8: Boxplot of Deaths per 100,000 from Air Pollution vs SDG Region

Interesting to note that Australia/New Zealand, Europe, North America seem to have the lowest deaths per 100k from air pollution and are all fairly compactly packed together (low variance) relative to other regions around the world. Furthermore, these region contain the most advanced countries.

Let’s take another look but at SubRegions.

Figure 9: Boxplot of Deaths per 100k from Air Pollution vs Sub Region

Separating out into an even granular grouping of regions show some trends where Australia/New Zealand, North America, Northern Europe, and Western Europe all have low deaths per 100k and have low variance. Historically, these regions consist of countries that have been considered ‘First World’ before our first year of analysis of 1990. We will dig into this more later in our SMART questions.

What does the GDP per capita of these regions look like comparatively? Let’s take a look.

Figure 10: Boxplot of GDP per Capita vs Sub Region

Interesting to observe that the same subregions that have low deaths caused by air pollution also have high GDP per capita comparatively. We will try to see if we can quantify this relationship later on in our main research analysis.

Map of Countries

Plotting maps and maps with intensities will be useful for us to visualize our data and the results of our analysis.

Figure 11: Global Map of SDGRegions and SubRegions

Figure 12: Global Intensity Map of Key Numerical Features, 1990 to 2017

Looks like some inverse correlation between gdp.per.capita and deaths.air.pollution.per.100k.

We can also use ggplot2 to have a bit more control over map plotting.

Figure 13: Global Intensity Map of Deaths due to Air Pollution per 100k People, 1990 to 2017

Figure 14: Intensity Map of Deaths due to Air Pollution per 100k People in East and Southeastern Asia, 2017

1. Is there a relationship between population size and Deaths per 100,000 due to air pollution?

Below, we would like to measure the relationship between Population size (in thousands) and Deaths per 100,000 due to air pollution. Since these variables are numerical, we have to confirm the normal distribution of both variables, and from the results below, we see that there is no correlation between a country’s population size and their deaths due to air pollution. we do observe a negative correlation between Deaths due to air pollution and GDP per Capita.

str(final_df)

## 'data.frame':    5197 obs. of  12 variables:
##  $ ISO.alpha2.code              : Factor w/ 248 levels "AD","AE","AF",..: 1 1 1 1 1 1 1 1 1 1 ...
##  $ M49.code                     : Factor w/ 249 levels "4","8","10","12",..: 6 6 6 6 6 6 6 6 6 6 ...
##  $ Year                         : Factor w/ 28 levels "1990","1991",..: 23 24 1 2 3 4 5 6 7 8 ...
##  $ ISO.alpha3.code              : Factor w/ 197 levels "","AFG","AGO",..: 5 5 5 5 5 5 5 5 5 5 ...
##  $ Country.x                    : Factor w/ 231 levels "Afghanistan",..: 6 6 6 6 6 6 6 6 6 6 ...
##  $ Deaths.Air.Pollution.per.100k: num  17.7 17.2 29 28.7 28.5 ...
##  $ GDP.USD                      : num  3188808943 3193704343 1029048482 1106928583 1210013652 ...
##  $ SDGRegion                    : Factor w/ 9 levels "AUSTRALIA/NEWZEALAND",..: 4 4 4 4 4 4 4 4 4 4 ...
##  $ SubRegion                    : Factor w/ 22 levels "AUSTRALIA/NEWZEALAND",..: 19 19 19 19 19 19 19 19 19 19 ...
##  $ Population.thousands         : num  82 81 55 57 59 61 63 64 64 64 ...
##  $ geom                         :sfc_MULTIPOLYGON of length 5197; first list element:  list()
##   ..- attr(*, "class")= chr [1:3] "XY" "MULTIPOLYGON" "sfg"
##  $ gdp.per.capita               : num  38887914 39428449 18709972 19419800 20508706 ...

#check normality
qqnorm(final_df$Population.thousands)

qqnorm(final_df$Deaths.Air.Pollution.per.100k)

cor(final_df$Population.thousands, final_df$Deaths.Air.Pollution.per.100k, method = c("spearman"))

## [1] 0.037

#correlation matrix
pop_poll_cor<- cor(select(final_df, Deaths.Air.Pollution.per.100k, Population.thousands, gdp.per.capita,))
pop_poll_cor

##                               Deaths.Air.Pollution.per.100k
## Deaths.Air.Pollution.per.100k                         1.000
## Population.thousands                                  0.069
## gdp.per.capita                                       -0.543
##                               Population.thousands gdp.per.capita
## Deaths.Air.Pollution.per.100k                0.069         -0.543
## Population.thousands                         1.000         -0.040
## gdp.per.capita                              -0.040          1.000

xkabledply(pop_poll_cor)

#plot
loadPkg("corrplot")
corrplot(pop_poll_cor)

2. Which countries had the highest and lowest deaths due to air pollution from 1990 - 2017? How is this related to the region?

library("data.table")
library(scales)
library(scales)

#Aggregate data by total deaths by country
deathsbyyear_c <- group_by(.data = final_df, Country.x)
totdeath_c <- summarize(.data = deathsbyyear_c, total = sum(Deaths.Air.Pollution.per.100k, na.rm = TRUE))
str(totdeath_c)

## tibble [193 × 2] (S3: tbl_df/tbl/data.frame)
##  $ Country.x: Factor w/ 231 levels "Afghanistan",..: 1 2 3 4 6 7 8 9 10 12 ...
##  $ total    : num [1:193] 3644 1660 1503 1088 592 ...

topdeaths_c <- totdeath_c[order(totdeath_c$total, decreasing = TRUE), ]  # Top N highest values by group
topdeaths_c <- data.table(topdeaths_c, key = "total")
topdeaths_c <- topdeaths_c[ , tail(.SD, 10)]
str(topdeaths_c)

## Classes 'data.table' and 'data.frame':   10 obs. of  2 variables:
##  $ Country.x: Factor w/ 231 levels "Afghanistan",..: 85 123 179 32 111 86 183 38 141 159
##  $ total    : num  5109 5218 5240 5386 5425 ...
##  - attr(*, ".internal.selfref")=<externalptr> 
##  - attr(*, "sorted")= chr "total"

air1 <- ggplot(data = topdeaths_c,
             mapping = aes(x = total, y = reorder(Country.x , total), color = "darkorange3")) +
      geom_segment(data = topdeaths_c,
               mapping = aes(x = 0, xend = total, y = reorder(Country.x, total), yend = Country.x)) +
      geom_point() +
          scale_x_continuous(limits = c(0, 7000), breaks = seq(0,7000,1000))
         # scale_color_manual(values = c("darkorange3", "firebrick1","lightpink1","green3","dodgerblue4","gold1")) 

air1 <- air1 + labs(title = "10 Countries with the Highest Deaths per 100,000",
                            subtitle = "Deaths due to Air Pollution, 1990 - 2017", 
                            caption = "Data Source: Kaggle",
                            x = "Deaths per 100,000",
                            y = "") +
         theme_minimal() +
        theme(axis.title = element_text(size = 8, face = "bold"),
        panel.grid.major.x = element_blank(),
        panel.grid.minor = element_blank(),
        panel.background = element_blank(),
        panel.grid.major.y = element_blank(),
        axis.line.x = element_line(color = "black"),
        axis.ticks = element_line(color = "black"),
        axis.text = element_text(size = 10),
        legend.position = "none",
        plot.subtitle = element_text(size = 8),
        plot.title = element_text(size = 10, margin = margin(b = 10)))

air1 <- air1 + theme(plot.title = element_text(color = "black", size = 12, face = "bold", hjust = 0),
                           plot.subtitle = element_text(color = "black", size = 10, hjust = 0 ),
                           plot.caption = element_text(color = "black", size =8, face = "italic", hjust =0))
air1

##Top 50 with lowest
lowdeaths_c <- totdeath_c[order(totdeath_c$total, decreasing = FALSE), ]  # Top N lowest values by group
lowdeaths_c <- data.table(lowdeaths_c, key = "total")
lowdeaths_c <- lowdeaths_c[ , head(.SD, 10)]
str(lowdeaths_c)

## Classes 'data.table' and 'data.frame':   10 obs. of  2 variables:
##  $ Country.x: Factor w/ 231 levels "Afghanistan",..: 184 199 144 95 73 104 12 35 74 219
##  $ total    : num  233 440 446 462 466 ...
##  - attr(*, ".internal.selfref")=<externalptr> 
##  - attr(*, "sorted")= chr "total"

air2 <- ggplot(data = lowdeaths_c,
             mapping = aes(x = total, y = reorder(Country.x , -total, color = "green4"))) +
      geom_segment(data = lowdeaths_c,
               mapping = aes(x = 0, xend = total, y = reorder(Country.x, -total), yend = Country.x)) +
      geom_point() +
          scale_x_continuous(limits = c(0, 7000), breaks = seq(0,7000,1000)) 
        #  scale_color_manual(values = c("darkorange3", "firebrick1","lightpink1","green3","dodgerblue4","gold1", "mediumorchid1", "azure4","sienna3")) 

air2 <- air2 + labs(title = "Countries with the Lowest Deaths per 100,000",
                            subtitle = "Deaths due to Air Pollution, 1990 - 2017", 
                            caption = "Data Source: Kaggle",
                            x = "dDeaths per 100,000",
                            y = "") +
         theme_minimal() +
        theme(axis.title = element_text(size = 8, face = "bold"),
        panel.grid.major.x = element_blank(),
        panel.grid.minor = element_blank(),
        panel.background = element_blank(),
        panel.grid.major.y = element_blank(),
        axis.line.x = element_line(color = "black"),
        axis.ticks = element_line(color = "black"),
        axis.text = element_text(size = 10),
        legend.position = "none",
        plot.subtitle = element_text(size = 8),
        plot.title = element_text(size = 10, margin = margin(b = 10)))

air2 <- air2 + theme(plot.title = element_text(color = "black", size = 12, face = "bold", hjust = 0),
                           plot.subtitle = element_text(color = "black", size = 10, hjust = 0 ),
                           plot.caption = element_text(color = "black", size =8, face = "italic", hjust =0))
air2

3. Which regions have the lowest and highest deaths due to air pollution?

library(scales)
#Aggregate data by total deaths by year and region 
deathsbyyear_reg <- group_by(.data = final_df,Year, SDGRegion)
totdeath_reg <- summarize(.data = deathsbyyear_reg, total = sum(Deaths.Air.Pollution.per.100k, na.rm = TRUE))
str(totdeath_reg)

## tibble [252 × 3] (S3: grouped_df/tbl_df/tbl/data.frame)
##  $ Year     : Factor w/ 28 levels "1990","1991",..: 1 1 1 1 1 1 1 1 1 2 ...
##  $ SDGRegion: Factor w/ 9 levels "AUSTRALIA/NEWZEALAND",..: 1 2 3 4 5 6 7 8 9 1 ...
##  $ total    : num [1:252] 50.5 1759.9 1290.9 1540.6 2272.3 ...
##  - attr(*, "groups")= tibble [28 × 2] (S3: tbl_df/tbl/data.frame)
##   ..$ Year : Factor w/ 28 levels "1990","1991",..: 1 2 3 4 5 6 7 8 9 10 ...
##   ..$ .rows: list<int> [1:28] 
##   .. ..$ : int [1:9] 1 2 3 4 5 6 7 8 9
##   .. ..$ : int [1:9] 10 11 12 13 14 15 16 17 18
##   .. ..$ : int [1:9] 19 20 21 22 23 24 25 26 27
##   .. ..$ : int [1:9] 28 29 30 31 32 33 34 35 36
##   .. ..$ : int [1:9] 37 38 39 40 41 42 43 44 45
##   .. ..$ : int [1:9] 46 47 48 49 50 51 52 53 54
##   .. ..$ : int [1:9] 55 56 57 58 59 60 61 62 63
##   .. ..$ : int [1:9] 64 65 66 67 68 69 70 71 72
##   .. ..$ : int [1:9] 73 74 75 76 77 78 79 80 81
##   .. ..$ : int [1:9] 82 83 84 85 86 87 88 89 90
##   .. ..$ : int [1:9] 91 92 93 94 95 96 97 98 99
##   .. ..$ : int [1:9] 100 101 102 103 104 105 106 107 108
##   .. ..$ : int [1:9] 109 110 111 112 113 114 115 116 117
##   .. ..$ : int [1:9] 118 119 120 121 122 123 124 125 126
##   .. ..$ : int [1:9] 127 128 129 130 131 132 133 134 135
##   .. ..$ : int [1:9] 136 137 138 139 140 141 142 143 144
##   .. ..$ : int [1:9] 145 146 147 148 149 150 151 152 153
##   .. ..$ : int [1:9] 154 155 156 157 158 159 160 161 162
##   .. ..$ : int [1:9] 163 164 165 166 167 168 169 170 171
##   .. ..$ : int [1:9] 172 173 174 175 176 177 178 179 180
##   .. ..$ : int [1:9] 181 182 183 184 185 186 187 188 189
##   .. ..$ : int [1:9] 190 191 192 193 194 195 196 197 198
##   .. ..$ : int [1:9] 199 200 201 202 203 204 205 206 207
##   .. ..$ : int [1:9] 208 209 210 211 212 213 214 215 216
##   .. ..$ : int [1:9] 217 218 219 220 221 222 223 224 225
##   .. ..$ : int [1:9] 226 227 228 229 230 231 232 233 234
##   .. ..$ : int [1:9] 235 236 237 238 239 240 241 242 243
##   .. ..$ : int [1:9] 244 245 246 247 248 249 250 251 252
##   .. ..@ ptype: int(0) 
##   ..- attr(*, ".drop")= logi TRUE

deaths_line <- ggplot() +
               geom_line(data = totdeath_reg, mapping = aes(x = Year, y = total, group = SDGRegion, color = SDGRegion), size = 1.2) +
              geom_point(data = totdeath_reg, mapping = aes(x = Year, y = total, group = SDGRegion, color = SDGRegion), size = 1.2) +
              scale_y_continuous(label = comma, limits = c(0, 15000), breaks = seq(0,15000,1500))
              # scale_x_discrete(limits = c(1990, 2017), breaks = seq(1990,2017,2)) 
deaths_line <- deaths_line + labs(title = "Deaths per 100,000 by Air Pollution, by Region",
                                            subtitle = "1990 - 2017", 
                                            caption = "Data Source: Kaggle",
                                            y = "Deaths due to Air Pollution",
                                            x = "") +
              theme_minimal() +
              theme(axis.title = element_text(size = 8, face = "bold"),
                    panel.grid.major.x = element_blank(),
                    panel.grid.minor = element_blank(),
                    panel.background = element_blank(),
                    panel.grid.major.y = element_blank(),
                    axis.line.x = element_line(color = "black"),
                    axis.ticks = element_line(color = "black"),
                    axis.text = element_text(size = 10),
                    #legend.position = "none",
                    legend.text = element_text(size=5),
                    plot.subtitle = element_text(size = 8),
                    plot.title = element_text(size = 10, margin = margin(b = 10)))
            
            deaths_line <- deaths_line + theme(plot.title = element_text(color = "black", size = 12, face = "bold", hjust = 0),
                                         plot.subtitle = element_text(color = "black", size = 10, hjust = 0 ),
                                         plot.caption = element_text(color = "black", size =8, face = "italic", hjust =0))
            deaths_line

4. How does deaths due to air pollution increase over time? More specifically, are death rates in recent X amount of years higher than death rates from groups of X years before?

library(scales)
#Aggregate data by total deaths by year
deathsbyyear <- group_by(.data = final_df,Year)
totdeath <- summarize(.data = deathsbyyear, tot_deaths = sum(Deaths.Air.Pollution.per.100k, na.rm = TRUE))
str(totdeath)

## tibble [28 × 2] (S3: tbl_df/tbl/data.frame)
##  $ Year      : Factor w/ 28 levels "1990","1991",..: 1 2 3 4 5 6 7 8 9 10 ...
##  $ tot_deaths: num [1:28] 18161 17803 17927 18133 18134 ...

deaths_line <- ggplot() +
               geom_line(data = totdeath, mapping = aes(x = Year, y = tot_deaths, group = 1), size = 1.2) +
              geom_point(data = totdeath, mapping = aes(x = Year, y = tot_deaths, group = 1), size = 1.2) +
              scale_color_manual(values = c("darkmagenta")) +
              scale_y_continuous(label = comma, limits = c(0, 40000), breaks = seq(0,40000,10000)) 
             # scale_x_discrete(limits = c(1990, 2017), breaks = seq(1990,2017,2)) 

deaths_line <- deaths_line + labs(title = "Deaths per 1000,000 by Air Pollution",
                                            subtitle = "1990 - 2017", 
                                            caption = "Data Source: Kaggle",
                                            y = "Deaths due to Air Pollution",
                                            x = "") +
              theme_minimal() +
              theme(axis.title = element_text(size = 8, face = "bold"),
                    panel.grid.major.x = element_blank(),
                    panel.grid.minor = element_blank(),
                    panel.background = element_blank(),
                    panel.grid.major.y = element_blank(),
                    axis.line.x = element_line(color = "black"),
                    axis.ticks = element_line(color = "black"),
                    axis.text = element_text(size = 10),
                    legend.position = "none",
                    plot.subtitle = element_text(size = 8),
                    plot.title = element_text(size = 10, margin = margin(b = 10)))
            
            deaths_line <- deaths_line + theme(plot.title = element_text(color = "black", size = 12, face = "bold", hjust = 0),
                                         plot.subtitle = element_text(color = "black", size = 10, hjust = 0 ),
                                         plot.caption = element_text(color = "black", size =8, face = "italic", hjust =0))
            deaths_line

## 'data.frame':    6468 obs. of  7 variables:
##  $ Entity                                         : chr  "Afghanistan" "Afghanistan" "Afghanistan" "Afghanistan" ...
##  $ Code                                           : chr  "AFG" "AFG" "AFG" "AFG" ...
##  $ Year                                           : int  1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 ...
##  $ Air.pollution..total...deaths.per.100.000.     : num  299 291 279 279 287 ...
##  $ Indoor.air.pollution..deaths.per.100.000.      : num  250 243 232 232 239 ...
##  $ Outdoor.particulate.matter..deaths.per.100.000.: num  46.4 46 44.2 44.4 45.6 ...
##  $ Outdoor.ozone.pollution..deaths.per.100.000.   : num  5.62 5.6 5.61 5.66 5.72 ...

Is there a correlation between GDP per capita and deaths caused by pollution? Is it linear? How strong is the correlation?

## 
## Call:
## lm(formula = log(Deaths.Air.Pollution.per.100k) ~ log(gdp.per.capita), 
##     data = final_df_sf)
## 
## Residuals:
##    Min     1Q Median     3Q    Max 
## -1.099 -0.235  0.000  0.206  1.431 
## 
## Coefficients:
##                     Estimate Std. Error t value            Pr(>|t|)    
## (Intercept)         10.07849    0.04871     207 <0.0000000000000002 ***
## log(gdp.per.capita) -0.38952    0.00323    -121 <0.0000000000000002 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.369 on 5195 degrees of freedom
## Multiple R-squared:  0.737,  Adjusted R-squared:  0.737 
## F-statistic: 1.45e+04 on 1 and 5195 DF,  p-value: <0.0000000000000002

## [1] 0.883

## [1] 0.887

## [1] 0.747

Is there a difference in means of death caused by pollution between low, mid, and high GDP per capita?

Let’s test if means of deaths caused by air pollution per 100k across different GDP per capita levels are not equal.

H₀: \(\mu\)_{deaths_lowest_gdp} = \(\mu\)_{deaths_low_gdp} = \(\mu\)_{deaths_medium_gdp} = \(\mu\)_{deaths_high_gdp}

H₁: At least one of \(\mu\)_{deaths_lowest_gdp}, \(\mu\)_{deaths_low_gdp}, \(\mu\)_{deaths_medium_gdp}, \(\mu\)_{deaths_high_gdp} is not equal

Use \(\alpha\) of 0.05.

The p-value_test1 is 0e+00, which is lower than \(\alpha\)_0.05. Therefore, we reject our null hypothesis that \(\mu\)_{deaths_lowest_gdp} = \(\mu\)_{deaths_low_gdp} = \(\mu\)_{deaths_medium_gdp} = \(\mu\)_{deaths_high_gdp}. This means that there is statistically significant that at least one of the means of deaths in low, medium, and high GDP per capita are not the same.

I will conduct 4 2-sample t-tests:

• Lowest GDP per capita’s deaths does not equal Low GDP per capita’s deaths
  • H₀: \(\mu\)_{deaths_lowest_gdp} = \(\mu\)_{deaths_low_gdp}
  • H₁: \(\mu\)_{deaths_lowest_gdp} != \(\mu\)_{deaths_low_gdp}
• Low GDP per capita’s deaths does not equal Medium GDP per capita’s deaths
  • H₀: \(\mu\)_{deaths_lowest_gdp} = \(\mu\)_{deaths_low_gdp}
  • H₁: \(\mu\)_{deaths_lowest_gdp} != \(\mu\)_{deaths_low_gdp}
• Medium GDP per capita’s deaths does not equal High GDP per capita’s deaths
  • H₀: \(\mu\)_{deaths_lowest_gdp} = \(\mu\)_{deaths_low_gdp}
  • H₁: \(\mu\)_{deaths_lowest_gdp} != \(\mu\)_{deaths_low_gdp}
• Lowest GDP per capita’s deaths does not equal High GDP per capita’s deaths
  • H₀: \(\mu\)_{deaths_lowest_gdp} = \(\mu\)_{deaths_low_gdp}
  • H₁: \(\mu\)_{deaths_lowest_gdp} != \(\mu\)_{deaths_low_gdp}

I will use a two sample t-test for each and use \(\alpha\) of 0.05.

Test 1:

p-value_test1: 2.99e-203

p-value_test1 < \(\alpha\)_0.05 = TRUE

Conclusion of test1: p-value_test1 is less than \(\alpha\)_0.05, therefore we reject our null hypothesis that \(\mu\)_{deaths_lowest_gdp} is equal to \(\mu\)_{deaths_low_gdp} and accept our alternative hypothesis.

Test 2:

p-value_test2: 1.47e-13

p-value_test2 < \(\alpha\)_0.05 = TRUE

Conclusion of test2: p-value_test2 is less than \(\alpha\)_0.05, therefore we reject our null hypothesis that \(\mu\)_{deaths_low_gdp} is equal to \(\mu\)_{deaths_medium_gdp} and accept our alternative hypothesis.

Test 3:

p-value_test3: 0e+00

p-value_test3 < \(\alpha\)_0.05 = TRUE

Conclusion of test3: p-value_test3 is less than \(\alpha\)_0.05, therefore we reject our null hypothesis that \(\mu\)_{deaths_medium_gdp} is equal to \(\mu\)_{deaths_high_gdp} and accept our alternative hypothesis.

Test 4:

p-value_test4: 2.91e-06

p-value_test4 < \(\alpha\)_0.05 = TRUE

Conclusion of test4: p-value_test4 is less than \(\alpha\)_0.05, therefore we reject our null hypothesis that \(\mu\)_{deaths_lowest_gdp} is equal to \(\mu\)_{deaths_high_gdp} and accept our alternative hypothesis.